Cu-2.2wt%Ni-0.5wt%Si alloy single crystals were grown by the Bridgman method and aged at 723 K for 10 h to form Ni2Si precipitates. Fully reversed tension-compression fatigue tests were conducted on the aged single crystals with a single slip orientation under constant plastic-strain amplitudes at room temperature. Cyclic softening occurred at plastic-strain amplitudes between 2.5x10-4 and 2.5x10-2. Using the maximum stress amplitude in each cyclic hardening/softening curve, a pseudo cyclic stress-strain curve (CSSC) was obtained. The CSSC was found to exhibit a plateau region with a stress level of about 167 MPa. Transmission electron microscopic observation revealed the formation of persistent slip bands (PSBs) in the plateau regime. It was found that the Ni2Si precipitate particles were intensively sheared by glide dislocations within the PSBs and were eventually re-dissolved into the Cu matrix. The macroscopic cyclic softening can be attributed to the local softening induced by the re-dissolution of the Ni2Si particles in the PSBs.